Karl Pearson’s coefficient of skewness for a data set Is -0.6. If me

1.	Karl Pearson’s coefficient of skewness for a data set Is -0.6. If mean = 60 and s = 10, find median and mode for the data.
Answer» Here, j = -0.60 x̄ = 60 s = 10 Mode: j = \(\frac{\bar x−M_o}{s}\) ∴ – 0.60 = \(\frac{60−M_0}{10}\) ∴ -0.60 × 10 = 60 – M₀ ∴ -6 = 60 – M₀ ∴ M₀ = 60 +6 = 66 Therefore, mode = 66. Median: M₀ = 3M – 2x ∴66 = 3M – 2 (60) ∴ 66 = 3M – 120 ∴ 66 + 120 = 3M ∴ 3M = 186 ∴ M = \(\frac{186}{3}\) Therefore, median = 62

Karl Pearson’s coefficient of skewness for a data set Is -0.6. If mean = 60 and s = 10, find median and mode for the data.

Answer»

Here, j = -0.60 x̄ = 60 s = 10

Mode:

j = \(\frac{\bar x−M_o}{s}\)

∴ – 0.60 = \(\frac{60−M_0}{10}\)

∴ -0.60 × 10 = 60 – M₀

∴ -6 = 60 – M₀

∴ M₀ = 60 +6 = 66

Therefore, mode = 66.

Median:

M₀ = 3M – 2x

∴66 = 3M – 2 (60)

∴ 66 = 3M – 120

∴ 66 + 120 = 3M

∴ 3M = 186

∴ M = \(\frac{186}{3}\)

Therefore, median = 62